There is a large gap between the engineering course of tensor algebra on the one side and the treatment of linear transformations within classical linear algebra on the other side. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book is addressed primarily to engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling an autonomous study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.
Table of contents:
Vectors and tensors in a finite-dimensional space.- Vector and tensor analysis in Euclidean space.- Curves an surfaces in three-dimensional Euclidean space.- Eigenvalue problem and spectral decomposition of second-order tensors.- Fourth-order tensors.- Analysis of tensor functions.- Analytic tensor functions.- Application to continuum mechanics.- Solutions.- References.- Index.
Table of contents:
Vectors and tensors in a finite-dimensional space.- Vector and tensor analysis in Euclidean space.- Curves an surfaces in three-dimensional Euclidean space.- Eigenvalue problem and spectral decomposition of second-order tensors.- Fourth-order tensors.- Analysis of tensor functions.- Analytic tensor functions.- Application to continuum mechanics.- Solutions.- References.- Index.